Bruce: There's nothing out there for me.
Alfred: And that's the problem. You hung up your cape and your cowl, but you didn't move on, you never went to find a life, to find someone...
Bruce: Alfred... I did find someone.
Alfred: I know, and you lost her. But that's all part of living, sir. But you're not living.

You're both not quite right.

Personally, Bruce didn't try to live, but publicly Bruce Wayne was still active for several years after Batman's disappearance.